Type-II multiferroism and linear magnetoelectric coupling in the honeycomb Fe4Ta2O9 antiferromagnet

Among the numerous exotic phenomena exhibited by honeycomb antiferromagnets, linear magnetoelectricity in niobiates and tantalates of an ${A}_{4}{M}_{2}{\mathrm{O}}_{9}$ formula has been attracting a lot of attention. The magnetic frustration, first exploited in $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{C}{\mathrm{r}}_{2}{\mathrm{O}}_{3}$ in the 1960s, can be tuned in the ``429'' compounds of which structures derive from corundum, by varying the $3d$ orbitals filling (from $3{d}^{5}$ to $3{d}^{7}$ as A goes from $\mathrm{M}{\mathrm{n}}^{2+}$ to $\mathrm{C}{\mathrm{o}}^{2+}$) and/or the size of the ${d}^{0}$M cation ($\mathrm{N}{\mathrm{b}}^{5+}$ or $\mathrm{T}{\mathrm{a}}^{5+}$). $\mathrm{F}{\mathrm{e}}_{4}\mathrm{T}{\mathrm{a}}_{2}{\mathrm{O}}_{9}$ illustrates the physics richness of these compounds, as it exhibits a rare combination of multiferroism and linear magnetoelectricity associated to different magnetic field dependences of the electrical polarization.